# Properties

 Label 128.4.b Level $128$ Weight $4$ Character orbit 128.b Rep. character $\chi_{128}(65,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $5$ Sturm bound $64$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$128 = 2^{7}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 128.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$64$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(128, [\chi])$$.

Total New Old
Modular forms 56 12 44
Cusp forms 40 12 28
Eisenstein series 16 0 16

## Trace form

 $$12 q - 108 q^{9} + O(q^{10})$$ $$12 q - 108 q^{9} - 104 q^{17} - 388 q^{25} + 464 q^{33} - 552 q^{41} + 2028 q^{49} + 16 q^{57} - 416 q^{65} + 1752 q^{73} - 3332 q^{81} + 1432 q^{89} + 1624 q^{97} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(128, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
128.4.b.a $2$ $7.552$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-64$$ $$q+2iq^{3}-3iq^{5}-2^{5}q^{7}-37q^{9}+\cdots$$
128.4.b.b $2$ $7.552$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-2})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{3}+19q^{9}+5^{2}\beta q^{11}-90q^{17}+\cdots$$
128.4.b.c $2$ $7.552$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{5}+3^{3}q^{9}+23iq^{13}+94q^{17}+\cdots$$
128.4.b.d $2$ $7.552$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$64$$ $$q+2iq^{3}+3iq^{5}+2^{5}q^{7}-37q^{9}+\cdots$$
128.4.b.e $4$ $7.552$ $$\Q(\sqrt{2}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+\beta _{3}q^{5}+\beta _{2}q^{7}-13q^{9}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(128, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(128, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(8, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 2}$$